Problem: Nastya likes reading and even spends whole days in a library sometimes. Today she found a chronicle of Byteland in the library, and it stated that there lived shamans long time ago. It is known that at every moment there was exactly one shaman in Byteland, and there were n shamans in total enumerated with integers from 1 to n in the order they lived. Also, each shaman had a magic power which can now be expressed as an integer.

The chronicle includes a list of powers of the n shamans. Also, some shamans can be king-shamans, if they gathered all the power of their predecessors, i.e. their power is exactly the sum of powers of all previous shamans. Nastya is interested in whether there was at least one king-shaman in Byteland.

Unfortunately many of the powers are unreadable in the list, so Nastya is doing the following:

  * Initially she supposes some power for each shaman. 
  * After that she changes the power of some shaman q times (the shamans can differ) and after that wants to check if there is at least one king-shaman in the list. If yes, she wants to know the index of any king-shaman. 



Unfortunately the list is too large and Nastya wants you to help her.

Input

The first line contains two integers n and q (1 ≤ n, q ≤ 2·105).

The second line contains n integers a1, ..., an (0 ≤ ai ≤ 109), where ai is the magic power of the i-th shaman.

After that q lines follow, the i-th of them contains two integers pi and xi (1 ≤ pi ≤ n, 0 ≤ xi ≤ 109) that mean that the new power of the pi-th shaman is xi.

Output

Print q lines, the i-th of them should contain  - 1, if after the i-th change there are no shaman-kings, and otherwise a single integer j, where j is an index of some king-shaman after the i-th change.

If there are multiple king-shamans after each change, print the index of any of them.

Examples

Input

2 1
1 3
1 2


Output

-1


Input

3 4
2 2 3
1 1
1 2
2 4
3 6


Output

3
2
-1
3


Input

10 7
0 3 1 4 6 2 7 8 10 1
2 5
1 3
9 36
4 10
4 9
1 2
1 0


Output

1
-1
9
-1
4
-1
1

Note

In the first example powers of shamans after the first change are equal to (2, 3). The answer equals  - 1, because the sum of powers of shamans before the first shaman is equal to 0, and before the second is equal to 2.

In the second example after the first change the powers are equal to (1, 2, 3). The answer is equal to 3, because the power of the third shaman is equal to 3, and the sum of powers of the first and the second shaman is also 1 + 2 = 3. After the second change the powers become equal to (2, 2, 3), where the answer equals 2. After the third change the powers become equal to (2, 4, 3), where the answer equals  - 1. After the fourth change the powers become equal to (2, 4, 6), where the answer equals 3.

Solution (in JAVA):

Solution:
//package round489;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class EX {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	// 1401
	void solve()
	{
		int n = ni(), Q = ni();
		int[] a = na(n);
		
		StarrySkyTreePosL sst = new StarrySkyTreePosL(n);
		sst.add(n, sst.H, 1000000000000000L);
		long sum = 0;
		for(int i = 0;i < n;i++){
			sst.add(i, i+1, sum-a[i]);
			sum += a[i];
		}
		
		for(int z = 0;z < Q;z++){
			int x = ni()-1, v = ni();
			int d = v - a[x];
			sst.add(x+1, n, d);
			sst.add(x, x+1, -d);
			a[x] = v;
			out.println(find0(sst));
		}
	}
	
	int[] inds = new int[100];
			
	int find0(StarrySkyTreePosL sst)
	{
		int p = 0;
		long B = 1000000000L*300000;
		while(sst.st[1] < 0){
			if(sst.st[1] < 0){
				inds[p++] = sst.pos[1];
				sst.add(sst.pos[1], sst.pos[1]+1, B);
			}
		}
		int ret = sst.st[1] == 0 ? sst.pos[1] + 1 : -1;
		for(int i = 0;i < p;i++){
			sst.add(inds[i], inds[i]+1, -B);
		}
		return ret;
	}
	
	public class StarrySkyTreePosL {
		public int M, H, N;
		public long[] st;
		public long[] plus;
		public int[] pos;
		public long I = Long.MAX_VALUE/4; // I+plus<int
		
		public StarrySkyTreePosL(int n)
		{
			N = n;
			M = Integer.highestOneBit(Math.max(n-1, 1))<<2;
			H = M>>>1;
			st = new long[M];
			plus = new long[H];
			pos = new int[M];
			for(int i = M-1;i >= H;i--)pos[i] = i-H;
			for(int i = H-1;i >= 0;i--)propagate(i);
		}
		
		public StarrySkyTreePosL(long[] a)
		{
			N = a.length;
			M = Integer.highestOneBit(Math.max(N-1, 1))<<2;
			H = M>>>1;
			st = new long[M];
			for(int i = 0;i < N;i++){
				st[H+i] = a[i];
			}
			plus = new long[H];
			Arrays.fill(st, H+N, M, I);
			pos = new int[M];
			for(int i = M-1;i >= H;i--)pos[i] = i-H;
			for(int i = H-1;i >= 1;i--)propagate(i);
		}
		
		private void propagate(int i)
		{
			if(st[2*i] <= st[2*i+1]){
				st[i] = st[2*i] + plus[i];
				pos[i] = pos[2*i];
			}else{
				st[i] = st[2*i+1] + plus[i];
				pos[i] = pos[2*i+1];
			}
		}
		
		public void add(int l, int r, long v){ if(l < r)add(l, r, v, 0, H, 1); }
		
		private void add(int l, int r, long v, int cl, int cr, int cur)
		{
			if(l <= cl && cr <= r){
				if(cur >= H){
					st[cur] += v;
				}else{
					plus[cur] += v;
					propagate(cur);
				}
			}else{
				int mid = cl+cr>>>1;
				if(cl < r && l < mid){
					add(l, r, v, cl, mid, 2*cur);
				}
				if(mid < r && l < cr){
					add(l, r, v, mid, cr, 2*cur+1);
				}
				propagate(cur);
			}
		}
		
		public long min(int l, int r){ return l >= r ? I : min(l, r, 0, H, 1);}
		
		private long min(int l, int r, int cl, int cr, int cur)
		{
			if(l <= cl && cr <= r){
				return st[cur];
			}else{
				int mid = cl+cr>>>1;
				long ret = I;
				if(cl < r && l < mid){
					ret = Math.min(ret, min(l, r, cl, mid, 2*cur));
				}
				if(mid < r && l < cr){
					ret = Math.min(ret, min(l, r, mid, cr, 2*cur+1));
				}
				return ret + plus[cur];
			}
		}
		
		public long[] minpos(int l, int r){ return l >= r ? null : minpos(l, r, 0, H, 1);}
		
		private long[] minpos(int l, int r, int cl, int cr, int cur)
		{
			if(l <= cl && cr <= r){
				return new long[]{st[cur], pos[cur]};
			}else{
				int mid = cl+cr>>>1;
				long[] L = null, R = null;
				if(cl < r && l < mid){
					L = minpos(l, r, cl, mid, 2*cur);
				}
				if(mid < r && l < cr){
					R = minpos(l, r, mid, cr, 2*cur+1);
				}
				if(L == null && R == null)return null;
				if(R == null || L[0] <= R[0]){
					L[0] += plus[cur];
					return L;
				}else{
					R[0] += plus[cur];
					return R;
				}
			}
		}
		
		public void fall(int i)
		{
			if(i < H){
				if(2*i < H){
					plus[2*i] += plus[i];
					plus[2*i+1] += plus[i];
				}
				st[2*i] += plus[i];
				st[2*i+1] += plus[i];
				plus[i] = 0;
			}
		}
		
		public int firstle(int l, long v) {
			if(l >= H)return -1;
			int cur = H+l;
			for(int i = 1, j = Integer.numberOfTrailingZeros(H)-1;i <= cur;j--){
				fall(i);
				i = i*2 + (cur>>>j&1);
			}
			while(true){
				fall(cur);
				if(st[cur] <= v){
					if(cur < H){
						cur = 2*cur;
					}else{
						return cur-H;
					}
				}else{
					cur++;
					if((cur&cur-1) == 0)return -1;
					cur = cur>>>Integer.numberOfTrailingZeros(cur);
				}
			}
		}
		
		public int lastle(int l, long v) {
			if(l < 0)return -1;
			int cur = H+l;
			for(int i = 1, j = Integer.numberOfTrailingZeros(H)-1;i <= cur;j--){
				fall(i);
				i = i*2 + (cur>>>j&1);
			}
			while(true){
				fall(cur);
				if(st[cur] <= v){
					if(cur < H){
						cur = 2*cur+1;
					}else{
						return cur-H;
					}
				}else{
					if((cur&cur-1) == 0)return -1;
					cur = cur>>>Integer.numberOfTrailingZeros(cur);
					cur--;
				}
			}
		}		
		public long[] toArray() { return toArray(1, 0, H, new long[H]); }
		
		private long[] toArray(int cur, int l, int r, long[] ret)
		{
			if(r-l == 1){
				ret[cur-H] = st[cur];
			}else{
				toArray(2*cur, l, l+r>>>1, ret);
				toArray(2*cur+1, l+r>>>1, r, ret);
				for(int i = l;i < r;i++)ret[i] += plus[cur];
			}
			return ret;
		}
	}
	
	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new EX().run(); }
	
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}